Generalized equivalence of matrices over Prüfer domains

Frank DeMeyer and Hainya Kakakhail

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-9

Abstract:

Two m × n matrices A , B over a commutative ring R are equivalent in case there are invertible matrices P , Q over R with B = P A Q . While any m × n matrix over a principle ideal domain can be diagonalized, the same is not true for Dedekind domains. The first author and T. J. Ford introduced a coarser equivalence relation on matrices called homotopy and showed any m × n matrix over a Dedekind domain is homotopic to a direct sum of 1 × 2 matrices. In this article give, necessary and sufficient conditions on a Prüfer domain that any m × n matrix be homotopic to a direct sum of 1 × 2 matrices.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:379318

DOI: 10.1155/S0161171291000881

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